This follows directly from Proposition REF  and [1]}.
Explicitly, a strong connection can be defined iteratively by
\(\ell (\mathbf {1}) = \mathbf {1}\otimes \mathbf {1} , \qquad \ell (t^n) = {\left\lbrace \begin{array}{ll}z_1^\ast \star _\theta \ell \left(t^{n-1}\right)\star _\theta z_1 + z_2^\ast \star _\theta \ell \left(t^{n-1}\right)\star _\theta z_2,& \text{for } n>0 ,\\z_1\star _\theta \ell \left(t^{n+1}\right)\star _\theta z^\ast _1 + z_2\star _\theta \ell \left(t^{n+1}\right)\star _\theta z_2^\ast ,& \text{for } n<0 ,\end{array}\right.}\) 
